1. Field of the Invention
The present invention relates to an optimized method for modelling the stratigraphic structure of an underground zone allowing fast adjustment of the parameters of the model with observed or measured data.
2. Description of the Prior Art
Sedimentary basins evolve over the course of time. They have a variable geometry under the effect of compaction (the pore volume decreases), subsidence (basin bottom deformation) and erosion (removal of part of the upper sediments of the basin). In a marine environment, sediments settle on the bottom and form a sedimentary basin. Estimation of the sediment height and the lithologic contents under the influence of compaction, subsidence and erosion is desirable.
The following notations are used to define all the parameters involved in the definition and the formation of such a sedimentary basin:
.OMEGA. Space studied that represents the sedimentary basin, .OMEGA..OR right.IR.sup.2. PA0 N Number of lithologies, N.gtoreq.1. PA0 E.sub.water.sup.1 Water efficiency, (unit: [.phi.] depending on the lithology l). PA0 q.sub.1, l=1, . . . , N: Sedimentary flow of the lithology l on the boundary of the space, it depends on time, (unit: [L.sup.2 T.sup.-1 ], L is the length and T the time). PA0 v.sub.1, l=1, . . . , N : Lithology l content, it depends on time, (unit: [.phi.]). PA0 Q.sub.L, l=1, . . . ,N: Sedimentary flow of the lithology l, (unit: [L.sup.2 T.sup.-1 ]). PA0 H(x,y,t): Height of the sediment, (unit: [L]). PA0 V.sub.s : Velocity of subsidence, (unit: [LT.sup.-1 ]). PA0 .PHI..sub.1 : Porosity, (unit: [.phi.]). PA0 K.sub.1 (h): Diffusion coefficient, also referred to as diffusivity, it depends on the space and time variables, (unit: [L.sup.2 T.sup.-1 ]). PA0 Equation for h: given by a mass conservation law. PA0 Equation for E.sub.water.sup.i ; it corresponds to the efficiency of the water (in transportation of sediments). PA0 Equation connected with the diffusion coefficient K.sub.i (h), it involves bathymetry and allows defining of the diffusion coefficient in relation to three different zones: continental, splash (tidal zone) and marine zone. The value of the diffusion coefficient will thus be defined from the three values K1 (K.sub.land), K2 (K.sub.bathy) and K3 (K.sub.sea) (FIG. 1) whose link between the continental and the marine zone is linear. PA0 Bornhotdt S., Optimization using Genetic Algorithms; Proceedings Numerical Experiments in Stratigraphy (NES) 1996. PA0 Lessenger M. et al.: Forward and Inverse Simulation Models of Stratal Architecture and Facies Distribution in Marine Shelf to Coastal Plain Environments. Thesis, Colorado School, November 1993, or by PA0 Lessenger M. et al.: Estimating Accuracy and Uncertainty of Stratigraphic Predictions from Inverse Numerical Models; in Proceedings Numerical Experiments in Stratigraphy (NES), 1996. PA0 calculating, by means of the direct model, the gradients of each quantity in relation to the parameters to be adjusted, and PA0 optimizing the model by minimizing, by successive iterations, a criterion function until a sufficient difference reduction is obtained, by calculating the sensitivity of the direct model to the parameters to be adjusted, so as to produce a stratigraphic representation of the underground zone. PA0 means for determining, by measurement or observation, a series of quantities representative of the stratigraphic structure of the zone at various points, and PA0 a data processing unit programmed for implementation of a direct initial model depending on a set of parameters representative of a geologic formation process of the zone, this processing unit including: PA0 means for determining, by means of the initial model, values taken by the quantities at the various measurement or observation points, PA0 means for calculating, from the direct model, gradients of each quantity in relation to the parameters to be adjusted, PA0 means for optimizing the model by minimizing, by successive iterations, a criterion function depending on said parameters, until a sufficient difference reduction is obtained, by calculating the sensitivity of the direct model to the parameters to be adjusted, and PA0 means for producing a stratigraphic representation of the underground zone.
The series of equations describing the sedimentation process are as follows:
Equation connecting the flow Q with the height h of the lithology i: Q.sub.i =-K.sub.i v.sub.i E.sub.water.sup.i.gradient.h, it is given by a flow law similar to Darcy's law.
In order to define the direct model of a basin, it is well-known to couple, for each lithology, transport equations with mass conservation equations so as to define, at each point of the basin, the rate of erosion or of sedimentation and the amount of each lithology.
The sedimentary basin is first represented by .OMEGA., open space of IR.sup.2 of boundary .GAMMA.=.GAMMA..sub.1 U.GAMMA..sub.2, and h,Q.sub.i and v.sub.i,i=1, . . . ,N are to be found such that: ##EQU1##
Functions g.sub.i can depend on the sedimentary supplies q.sub.i (production of carbonates, etc) or on the accomodation (velocity of subsidence V.sub.s, eustasy, compaction), etc. In cases where velocities V.sub.s are known and functions K.sub.i are bounded on .OMEGA. so that, for any i, we have .alpha..sub.i &gt;0 such that K.sub.i.gtoreq..alpha..sub.i, h will be solution to the parabolic equation as follows: ##EQU2##
where (f.sub.i (h)=-K.sub.i v.sub.i E.sub.water.sup.i).
In the field of geosciences, there are well-known inversion methods allowing constrain of an initial simulation model of an underground zone such as a sedimentary basin, resulting for example from a geostatistical simulation, by data observed or measured in the zone, according to an automatic iterative process.
Several techniques exist for solving inversion problems. A well-known trial-and-error technique consists in applying a genetic type optimization algorithm copied from the process of evolution by natural selection. An example of this technique applied to stratigraphic modelling of sedimentary basins is for example described by:
Implementation of this technique is easy and requires no gradient calculation. However, in certain numerical tests, on account of the random selection of the initial population, several generations and a large population are required to decrease the criterion function, this term designating the least-squares error between observations (reference values) and predictions (calculated values).
Another well-known method consists in using an iterative backward algorithm for parameter adjustment, assuming that the criterion function respects certain forms. A technique of this type, applied to stratigraphic modelling of sedimentary basins, is for example described by:
The Assignee's U.S. Pat. No. 5,844,799 also describes a manual type trial-and-error method that can be used in the case of a geologic parameter adjustment problem in a stratigraphic process, when one has good knowledge of the sedimentary deposit environment.